diff --git a/Eigen/src/OrderingMethods/Amd.h b/Eigen/src/OrderingMethods/Amd.h
index 63d996cb4..323255e0a 100644
--- a/Eigen/src/OrderingMethods/Amd.h
+++ b/Eigen/src/OrderingMethods/Amd.h
@@ -150,7 +150,7 @@ void minimum_degree_ordering(SparseMatrix<Scalar,ColMajor,StorageIndex>& C, Perm
       }
    
     d = degree[i];
-    if(d == 1)                      /* node i is empty */
+    if(d == 1 && has_diag)           /* node i is empty */
     {
       elen[i] = -2;                 /* element i is dead */
       nel++;
diff --git a/test/sparselu.cpp b/test/sparselu.cpp
index c725847d8..78615ff3b 100644
--- a/test/sparselu.cpp
+++ b/test/sparselu.cpp
@@ -41,9 +41,9 @@ template<typename T> void test_sparselu_T()
   SparseLU<SparseMatrix<T, ColMajor>, AMDOrdering<int> > sparselu_amd; 
   SparseLU<SparseMatrix<T, ColMajor, long int>, NaturalOrdering<long int> > sparselu_natural;
   
-  check_sparse_square_solving(sparselu_colamd); 
-  check_sparse_square_solving(sparselu_amd, 300, 2000, !true); // FIXME AMD ordering fails for structurally deficient matrices!
-  check_sparse_square_solving(sparselu_natural, 300, 2000, true);
+  check_sparse_square_solving(sparselu_colamd,  300, 100000, true); 
+  check_sparse_square_solving(sparselu_amd,     300,  10000, true);
+  check_sparse_square_solving(sparselu_natural, 300,   2000, true);
   
   check_sparse_square_abs_determinant(sparselu_colamd);
   check_sparse_square_abs_determinant(sparselu_amd);